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indecomposable filter Amenable C-sequence Rado's conjecture Sakurai's Bell inequality Lipschitz reduction Knaster club_AD Selective Ultrafilter stick PFA Parameterized proxy principle Local Club Condensation. Reduced Power diamond star Generalized Clubs Knaster and friends polarized partition relation regressive Souslin tree C-sequence strongly bounded groups middle diamond Distributive tree tensor product graph Strongly compact cardinal Intersection model approachability ideal Slim tree Ramsey theory over partitions Prikry-type forcing Rock n' Roll Ineffable cardinal Commutative projection system full tree 54G20 Martin's Axiom Microscopic Approach Partition Relations Successor of Regular Cardinal weak diamond Poset Absoluteness Countryman line square principles O-space Forcing Square-Brackets Partition Relations Generalized descriptive set theory Ascent Path Uniformization Coherent tree Small forcing Non-saturation incompactness Constructible Universe Minimal Walks stationary hitting Diamond Open Access super-Souslin tree PFA(S)[S] Closed coloring positive partition relation Singular cofinality Subnormal ideal Iterated forcing Erdos-Hajnal graphs OCA Commutative cancellative semigroups Vanishing levels Was Ulam right? Strong coloring ccc Forcing with side conditions Singular cardinals combinatorics Filter reflection stationary reflection Postprocessing function Singular Density Diamond for trees Fast club Dushnik-Miller Luzin set Successor of Singular Cardinal Jonsson cardinal L-space HOD Uniformly homogeneous higher Baire space Diamond-sharp Greatly Mahlo Rainbow sets specializable Souslin tree Shelah's Strong Hypothesis Souslin Tree free Souslin tree nonmeager set Subadditive Almost-disjoint family unbounded function ZFC construction Nonspecial tree SNR Entangled linear order countably metacompact weak square Aronszajn tree Well-behaved magma Universal Sequences Reflecting stationary set Ostaszewski square Analytic sets Cohen real Mandelbrot set AIM forcing Hereditarily Lindelöf space Club Guessing Subtle tree property projective Boolean algebra very good scale Hindman's Theorem Dowker space Fat stationary set Ulam matrix Cardinal Invariants b-scale Sierpinski's onto mapping principle free Boolean algebra Chromatic number coloring number perfectly normal Almost countably chromatic Almost Souslin Antichain square Cardinal function Hedetniemi's conjecture Sigma-Prikry transformations Large Cardinals xbox reflection principles Axiom R Forcing Axioms Weakly compact cardinal Respecting tree Ascending path Foundations Strongly Luzin set Interval topology on trees Whitehead Problem Prevalent singular cardinals sap weak Kurepa tree Precaliber Uniformly coherent Erdos Cardinal Kurepa Hypothesis S-Space GMA Subtle cardinal Fodor-type reflection Monotonically far P-Ideal Dichotomy Chang's conjecture
Tag Archives: Entangled linear order
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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